Customers of the failed securities firm MF Global Holdings, who are awaiting the fate of $1.6 billion in missing client money, have received an offer for their funds from Barclays Capital that would make them nearly whole.

The US unit of the British bank has offered to pay customers with US accounts 90 percent of their entire claim in exchange for the right to any additional funds that might be returned, according to people familiar with the matter.

That figure is above the 72 percent customers have received so far from the trustee unwinding MF Global’s brokerage unit.

The bank also offered to pay customers with foreign accounts 65 percent of their claims, a person familiar with the situation said. Those customers have not received any of their funds back so far.

Separately, Royal Bank of Scotland (RBS) indicated it would offer an even higher value for claims, but only for those held by institutions, according to people familiar with the matter and a term sheet.

RBS is offering 91 cents on the dollar for US accounts and 66 cents on the dollar for foreign accounts.

The offers from the banks, which customers can choose to accept or decline, offer a new avenue for MF Global customers, who have been awaiting the fate of their missing funds since the securities firm filed for Chapter 11 protection last October.

The offers were negotiated with a group of representatives from the Commodity Customer Coalition, an umbrella group made up of MF Global customers and led by Chicago fund manager James Koutoulas, according to people familiar with the matter.

Representatives for both Barclays and RBS declined to comment.

Several banks and investment firms have been buying up MF Global customer claims in recent weeks, according to court filings. Such buyers routinely trade claims made in bankruptcy court and other so-called distressed assets, offering a portion of a creditor’s claim now in hopes for a bigger payout down the road.

The bids are similar to the market for claims that emerged following the collapse of Bernard Madoff’s investment-advisory firm and the bankruptcy of Lehman Brothers Holdings. Speculators have been transacting in claims to funds in both cases, with the expectation that additional funds will be available later.

In the case of Barclays and RBS, the banks are acting as market makers by purchasing the accounts with the goal of selling them to third-party investors, such as hedge funds, according to people familiar with the matter.

Accepting the offer presents risks to customers. Although they might receive additional funds in the short term, they forfeit the right to any additional cash — perhaps the remainder — that investigators might turn up later.